A positive displacement apparatus comprising a pair of combinations of a hollow circular cylindrical vane guide and a single vane rotatable about an axis eccentrically disposed within the vane guide, which vane engages and extends through a slotted axial opening included in the cylindrical wall of the hollow circular cylindrical vane guide, has been invented by one of the inventors of the present invention and disclosed in a U.S. patent application Ser. No. 846,698. The positive displacement apparatus comprising the pair of combinations of the vane guide and the single vane requires two cylindrical cavities respectively housing the pair of combinations of the vane guide and the single vane, and a gearing that couples the rotating motions of the two vanes respectively included in the pair of combinations of the vane guide and the single vane. A simpler version of the positive displacement apparatus employing the combination of the vane guide and the vanes can be constructed by employing a single combination of the hollow circular cylindrical vane guide and a plurality of vanes rotatably mounted on a shaft eccentrically disposed within the vane guide and radially extending through a plurality of slotted axial openings included in the cylindrical wall of the vane guide.